Persuasive speeches are those where one tries to persuade or convince a group of people. These speeches aim to influence and change the opinions of the audience. This can be a difficult task as you would be facing a group of people who may have totally opposite views from your own. The most important point that has to be kept in mind here is that if you want to influence others' views and ideas, you have to show your enthusiasm while speaking.
However, you must remember that you are not there to wage a war and should talk without hurting others' feelings. Persuasive speeches are often given by sales and marketing people to attract interest in their products. They are also used to influence political and religious views.